The authors investigated the 3s²ns ²S Rydberg series and salient features of the 3s²nd ²D_{3/2, 5/2}, series in free aluminium atoms. The high ²D and ²S levels were populated by stepwise excitation using 4s ²S_1/2 as the intermediate state. They determined the position of the series members accurately from the normally forbidden 4s ²S-ns ²S and 4s ²S-nd ²D transitions (37<or=n<or=55) in a weak electric field. The ²S series is not perturbed; its quantum defect is 1.729(2). The ²D series is strongly perturbed by interaction with the ²D term of the 3s3p² configuration and with other configurations. A new value for the ionisation limit is derived: 48278.372(1) cm^-1. The fine-structure splitting of the high ²D levels has been estimated for the first time. The splitting is very large, due to a perturbation of the series. The authors' results are compared with other aluminium data as well as with data from the elements gallium and indium.